10 Activities for Finding Area and Circumference of a Circle

Area and circumference of a circle often gives our students their first taste of geometry during the year. Also, it seems like students see formulas for the first time when learning this topic. Usually, they don’t come to us understanding how to plug values into formulas. That means that we have to teach the idea of using formulas to them as well as how to find the area and circumference of a circle. Even though that can feel daunting, though, the great thing about circles and geometry is that they lend themselves to application pretty easily. We definitely have the opportunity to let students see area and circumference in a hands-on way. This post is full of engaging, fun area and circumference activities for secondary math students.

Sometimes I hear teachers talk about whether they should teach area first or circumference first. Personally, I believe you should teach them together and that student really need to understand the differences. Too often we have our students do things in isolation and later on they don’t know what to do because we go in a different order, or they have to apply their knowledge without knowing that a problem is an “area problem” or a “circumference problem”. The following list of activities will give your students lots of opportunities to practice working with and solving problems related to finding the area and circumference of circles.

Let’s dive in

As you read through this list you’ll notice that some activities work for bell ringers while other activities are whole class review games. You’ll find a wide range of activity types and possible uses for your classroom. Have fun exploring these engaging activities.

Students love mazes because they don’t have high stakes attached to them. It gives them a chance to practice in a relaxed way. We use mazes in my room every day as a bell ringer and I love the tone that it sets for the class.

This particular set of 3 mazes is one of my favorite. I love the fact that circles have pi in their formula and that pies are circles. That gives me a chance to use pies in my activities and kids love talking about pie. So, I get to use my pie clipart in these mazes. In one of the mazes students find the area area, in the next they find circumference, and the last one they find both area and circumference. Some of the answers are in terms of pi and other answers are using 3.14 as an approximation for pi.

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One of my favorite things to do is to inspire my colleagues to try new things. I work at a school where my 12 years of teaching is less than all of the other teachers in the math department. We are a veteran core. We all have a traditional streak in us and we have all tried to break out of that streak to get our students more engaged. One of my colleagues in particular used to tell me that she hated bingo. Then, just the other day when I went into her classroom she was playing bingo with her class. She even gave out some little prizes. It was amazing to see how even reluctant 8th graders worked hard for the prizes.

This area and circumference of circles bingo game is full of word problems. Students have to find area and circumference with different measurements and sometimes in terms of pi. Some of the questions are a little bit easier where they just have to find the diameter or radius. Each question is based off of a picture, like a guy holding 10 boxes of pizza, a dog catching a Frisbee, or a girl counting coins. I like to use this game for whole class review at the end of the unit. Try this game you’ll have your students practicing in a fun and engaging way.

This Area and Circumference Discovery Lab is one of my favorite. Discovery labs are a great way to introduce students to a topic and let them find patterns and draw conclusions. This helps them do the learning and have it more strongly anchored in their mind. What I’ve realized with discovery labs is that they have to be very focused and the students should not be trying to learn too many things at once. This lab focuses on identifying what the differences between area and circumference. Students will work to build their conceptual background of how circumference is one-dimensional and area is two-dimensional.

For this activity students color in the area and then use wikisticks or yarn to measure the circumference. They approximate the area using squares that are on the paper. We don’t use the formulas, yet. By counting the inch squares, students actually see why area is measured in square inches. This gives them a chance to really see what is happening when we talk about area and circumference. Then you always have an experience to lead them back to when they get that look on their face like, “Which one is area and which one is circumference, again?” You can read more in this step by step guide of how this activity walks students through this discovery process in this post.

You can either have the students cut the circles out, which takes them longer than it should, or they can just measure them on the paper. Also, you can have them label the circles with the different measurements or they can use a graphic organizer (included in the circles download) to analyze the various shapes.

Mnemonics work because our brains like structure. I don’t use a lot of them, but when I find one that helps kids remember something like the formulas for area and circumference of a circle, I’ll use that. Even though I’ve been finding area and circumference of a circle for a very long time, I still get the two formulas mixed up and have to stop and think about them.

Many students are in the same boat. Not to mention how important things like mnemonic devices are for students who need extra support. The students who struggle with executive function and organizing information in their brain really thrive when they have a way to remember. That’s where this great mnemonic strategy from Janine Huldie over on Owlcation comes in. I took that idea and created an insert for my students’ interactive notebooks.

The saying that students remember is:

Cherry pie is delicious!

Apple pies are too!

If they can remember that, then they can keep the two formulas straight. We use a graphic organizer (dowload FREE here) in our interactive notebook for this. Everyday, for a while, we practice writing the formulas on our whiteboard while saying this statement until they all have it. Sometimes it’s the little things that make a big difference.

This paper plate activity from The Reading Buddies brings in a little bit of art and a visual activity to your classroom. Students struggle sometimes to remember the parts of the circle. Creating their own colorful circle can help them remember. This activity walks through how to use paper plates to review the vocabulary and formulas we use when talking about area and circumference of a circle.

Also, you can have students share their plates with other people and get some math talk going. At the end of the activity they can hang their creations on the wall and do a gallery walk to look at other people’s plates. The blog post where I got this idea used this activity for Pi Day and has them decorate the plates like a pie. I think it can be used during Pi Day or any time of year when you have your unit on area and circumference of circles.

If you need an anticipatory set you might want to use this online circumference memory game. Students can play by themselves or with a partner. They have to find the circumference of 6 different circles and then play a memory matching game. It’s cute and it adds a little fun to their practice.

I love this online circle tool from Illuminations. It has three functions and you don’t have prep anything. It has an introduction screen, an investigation screen, and finally it has some practice problems. You can have it open on your computer and show the students what you want them to do on the screen in the front of the room. Then, students can work independently or in partners to to do the investigation and some practice problems.

When they finish the activity I would have them write a reflection of their experience using this tool. This is a great opportunity to find out what students understand about finding the area and circumference of circles. In addition, you can see some misconceptions, as well.

My kids love to review using whole class games. Jeopardy is one of the games we play periodically. This game of Jeopardy gives students practice in finding the radius, finding the diameter, and finding area and circumference. I don’t play Jeopardy in teams. When I play all students write their answers on a whiteboard or SmartPal. I find that if everyone has to write down the answers then they are more accountable. This activity is great for the day you introduce the topic or the day before the test.

Try one thing

We’ve presented a lot of ideas in this post. These activities can be used practice or review and will get your students engaged in practicing finding the area and circumference of a circle. My challenge to you is to just try one thing. Look through the list and try something new. I find that when I try something new it gets me more involved in the teaching. The students will appreciate it because they get tired of doing the same things over and over. So, good luck in your teaching or reviewing of this topic. Just remember, great teachers are always refining their craft. I hope you’ve found some activities or tools here that will help you take your area and circumference unit to the next level. Thanks for reading! Until next time.

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